document.write( "Question 1089863: If 40x^2 + 102x + c = (4x + 13)( ax + b) , what is the value of c? \n" ); document.write( "

Algebra.Com's Answer #704292 by EMStelley(208) $\"\"$ $\"About$

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$\"40x%5E2+%2B+102x+%2B+c+=+%284x+%2B+13%29%28ax+%2B+b%29\"$
\n" ); document.write( "Simplifying the right hand side, we have
\n" ); document.write( " $\"40x%5E2+%2B+102x+%2B+c+=+4ax%5E2+%2B+4bx+%2B+13ax+%2B+13b\"$
\n" ); document.write( " $\"40x%5E2+%2B+102x+%2B+c+=+4ax%5E2+%2B+%284b+%2B+13a%29x+%2B+13b\"$
\n" ); document.write( "Now, notice that we have an x^2 term on each side, an x term on each side, and a constant term on each side. Because the two sides are equal to each other, each of the individual terms must be equal. So, for the x^2 term, we have that:
\n" ); document.write( " $\"40x%5E2+=+4ax%5E2\"$
\n" ); document.write( " $\"a+=+10\"$
\n" ); document.write( "For the x term, we have:
\n" ); document.write( " $\"102x+=+%284b+%2B+13a%29x\"$
\n" ); document.write( " $\"102+=+4b+%2B+13\"$
\n" ); document.write( " $\"102%2F13+=+4b\"$
\n" ); document.write( " $\"b+=+102%2F52+=+51%2F26\"$
\n" ); document.write( "And lastly, for the constant term, we have:
\n" ); document.write( " $\"c+=+13b\"$
\n" ); document.write( "And we have a value for b, so
\n" ); document.write( " $\"c+=+13%2A%2851%2F26%29+=+51%2F2\"$ \n" ); document.write( "

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